Triangle Congruence

Front

What is Triangle Congruence?

Back

Triangle congruence refers to the condition where two triangles are considered congruent if they have the same size and shape, meaning their corresponding sides and angles are equal.

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What does AAS stand for in triangle congruence?

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AAS stands for Angle-Angle-Side, a method to prove triangle congruence where two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle.

Front

What is the Reflexive Property of Congruence?

Back

Front

What is the difference between SSS and SAS in triangle congruence?

Back

SSS (Side-Side-Side) states that if three sides of one triangle are equal to three sides of another triangle, they are congruent. SAS (Side-Angle-Side) states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, they are congruent.

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What does HL stand for in triangle congruence?

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HL stands for Hypotenuse-Leg, a method to prove congruence specifically for right triangles, where the hypotenuse and one leg of one triangle are equal to the hypotenuse and one leg of another triangle.

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How can you determine if two triangles are congruent using ASA?

Back

ASA stands for Angle-Side-Angle, which states that if two angles and the included side of one triangle are equal to two angles and the corresponding included side of another triangle, the triangles are congruent.

Front

What is the purpose of the Vertical Angles Theorem?

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The Vertical Angles Theorem states that when two lines intersect, the opposite (vertical) angles are equal, which can help in proving triangle congruence.

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What is the significance of the SSA condition in triangle congruence?

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SSA (Side-Side-Angle) does not guarantee triangle congruence because two different triangles can be formed with the same two sides and a non-included angle.

Front

If angle a + angle b = angle d, what can be inferred?

Back

If angle a and angle b add up to angle d, it indicates that angles a and b are complementary to angle d, which can be useful in solving for unknown angles.

Front

What is the definition of congruent triangles?

Back

Congruent triangles are triangles that are identical in shape and size, meaning all corresponding sides and angles are equal.